When does the Dordogne get crowded? Here's a clue:
2015: Went to Gouffre de Padirac during the last week of June. Walked right up and bought a ticket for the next tour (everyone is happy)
2017: Went to Gouffre de Padirac during the first week of July. Walked right up and bought a ticket, but for a tour leaving in 2 hours (everything before that was full, so we had to wait 2 hours, no biggie)
This week (2nd week of August 2017): Sold out for the entire week!
https://www.facebook.com/GouffreDePadirac/
To me, this is a good indicator of just how peaky the tourist season is in the Dordogne. My advice - study the European school calendar (Last day of school in France in 2017 was Friday, July 7th) and plan your trips (if you can) for when school is in session.